As first step towards the consideration of the associated control-estimator design problem, in this study the problem of drawing a low-order finite-dimensional DA model of the bi/tristable OPDE one of a spatially distributed throated biomass gasification reactors is addressed, with focus on the description of the practical steady state (SS) of highest conversion. The reactor is described by 15 nonlinear PDEs, which are numerically solved using finite differences to discretize the spatial domain. The number and placement of nodes along the axial direction of the reactor act as degrees of freedom that must be carefully chosen. In this study, a node location method, initially developed for a different class of reactors, is applied to the throated reactor. It was found that the desired SS can be effectively described by relocating some nodes using the adaptive mesh method, which results in a model order smaller than the case with an uniform node distribution. It was also observed that one must be mindful of the discretization near the air entrance, as excessive discretization in that zone can lead to poor descriptions of the desired SS or increase unnecessarily the model order (and consequently, the number of equations to be solved online). The results presented here lay the groundwork for improving the adaptive mesh location method to extend its application to throated gasifiers, thereby ensuring accurate numerical solutions for control and estimation tasks.